Observe that our results considerably extend the results obtained in [1]}, where only the case \(q=\frac{p}{2}\)  was considered. Of course for this instance we reobtain the results from [1]}. Further, our analysis reveals that the choice \(p=2q\)  in the dynamical system (REF ) is not necessarily optimal. Indeed, for a fixed \(q\)  we may obtain the convergence rate of order
\(O\left(\frac{1}{t^{\frac{4q+2}{3}}}\right)\)  for the decay \(g(x(t))-\min g\) , meanwhile in [1]} only the rate \(O\left(\frac{1}{t^{2q}}\right)\)  has been obtained. On the other hand, if we fix \(p\in ]0,2[\) , then for every \(q\in \left]\max \left(0,\frac{2p-1}{3}\right),1\right[\)  one has \(g(x(t))-\min g=O\left(\frac{1}{t^{p}}\right),\)  hence we can choose infinitely many damping coefficients in order to obtain the same convergence rate as in case \(q=\frac{p}{2}.\)  These features of our dynamical system (REF ) will also be underlined via some numerical experiments.
